Definition

Noun: A regular polyhedron is a three-dimensional geometric solid where all faces are identical regular polygons, and the same number of faces meet at every vertex. All its polyhedral angles are congruent. These are highly symmetrical shapes.

Usage and Examples

A regular polyhedron is a specific, well-defined geometric concept. * In geometry class, we studied the five Platonic solids, which are all regular polyhedra. * A cube is a common example of a regular polyhedron because all its faces are congruent squares. * The tetrahedron, with four equilateral triangle faces, is the simplest regular polyhedron.

Advanced Usage and Concepts

• Platonic Solids: The term regular polyhedron is synonymous with the five Platonic solids. These are the convex regular polyhedra that exist in three-dimensional space.
• Mathematical Properties: The study of regular polyhedra involves Euler's formula (V - E + F = 2), dihedral angles, and symmetry groups.

Variants and Related Words

• Polyhedron (n): A general solid figure with many plane faces, typically more than six. A regular polyhedron is a specific type of polyhedron.
• Platonic Solid (n): Another name for a convex regular polyhedron.
• Regular Polygon (n): A two-dimensional shape with all sides and angles equal, which forms the faces of a regular polyhedron.

Synonyms

• Platonic solid
• Regular convex polyhedron

Related Terms and Classifications

• The Five Regular Polyhedra:
  • Tetrahedron: 4 triangular faces.
  • Cube (Hexahedron): 6 square faces.
  • Octahedron: 8 triangular faces.
  • Dodecahedron: 12 pentagonal faces.
  • Icosahedron: 20 triangular faces.

Noun

1. any one of five solids whose faces are congruent regular polygons and whose polyhedral angles are all congruent